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$$ (f(g(x)))'=f'(g(x))\cdot g'(x)\\ \frac { d(f(g(x))) }{ d(x) } =\frac { d(f(g(x))) }{ d(g(x)) } \cdot \frac { d(g(x)) }{ dx } \\ and\quad defining:\\ y=g(x)\\ z=f(y),\quad we\quad will\quad have:\\ \frac { dz }{ dx } =\frac { dz }{ dy } \cdot \frac { dy }{ dx } \\ Generalizing:\\ \frac { d }{ dx } (f\circ g\circ h\circ i...)(x)=\frac { df }{ dg } \frac { dg }{ dh } \frac { dh }{ di } \frac { di }{ ... } ...\frac { ... }{ dx } $$
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